Interplay between degree and Boolean rules in the stability of Boolean networks

TL;DR

This paper investigates how the combination of network topology and Boolean rules influences the stability of biological Boolean networks, revealing that certain correlations and input properties can enhance robustness.

Contribution

It provides new insights into how degree and Boolean functions jointly affect network stability, emphasizing the role of sensitivity and canalizing inputs.

Findings

Negative correlation between sensitivity and degree improves stability.

Canalizing inputs amplify effects when linked to high-degree nodes.

Analytical predictions match numerical simulations.

Abstract

Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we study the joint effects of degree and Boolean functions on the stability of Boolean networks. To elucidate these effects, we focus on i) the correlation between the sensitivity of Boolean variables and the degree, and ii) the coupling between canalizing inputs and degree. We find that negatively correlated sensitivity with respect to local degree enhances the stability of Boolean networks against external perturbations. We also demonstrate that the effects of canalizing inputs can be amplified when they coordinate with high in-degree nodes. Numerical simulations confirm the accuracy of our analytical predictions at both the node and network levels.